Solve for $x$ : $6x^2 + 48x - 54 = 0$
Answer: Dividing both sides by $6$ gives: $ x^2 + {8}x {-9} = 0 $ The coefficient on the $x$ term is $8$ and the constant term is $-9$ , so we need to find two numbers that add up to $8$ and multiply to $-9$ The two numbers $9$ and $-1$ satisfy both conditions: $ {9} + {-1} = {8} $ $ {9} \times {-1} = {-9} $ $(x + {9}) (x {-1}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 9) (x -1) = 0$ $x + 9 = 0$ or $x - 1 = 0$ Thus, $x = -9$ and $x = 1$ are the solutions.